Finite Group Databasebeta

← #14283182

Subgroups — #14283182

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4070C211yesmaximal, characteristic
2C5×#4726C211yesmaximal, characteristic
3#11748719C211yesmaximal, characteristic
4#11746288C211yesmaximal, characteristic, complemented
5C3×#64687C211yesmaximal, characteristic, complemented
6#11745964C211yesmaximal, characteristic, complemented
7#11745960C211yesmaximal, characteristic, complemented
8#10600773—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×D3×Dic10C411yescharacteristic, complemented
11#91813C2211yescharacteristic
12C2×C5×ΓL(1,𝔽25)—21no—
13C3×#4070C2211yescharacteristic
14#91575—21no—
15D3×C22⋊Dic5—21no—
16C2×(C2×D3)⋊Dic5—21no—
17C2×Dic3×Dic5—21no—
18D3×C4⋊Dic5C411yescharacteristic, complemented
19D3×#683—21no—
20#91369C411yescharacteristic, complemented
21#91365C411yescharacteristic, complemented
22#91352—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24#91115C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C5×(C2×D3)⋊C8—21no—
27C3×#3963C2211yescharacteristic
28#68335—51nomaximal, Hall
29C2×#4070—31no—
30C5×#407—31no—
31C4×C22⋊Dic5—31no—
32#64687—31no—
33#64687—31no—
34#64687—31no—
35#64687D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30C2×C411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C2×C4×C5×D3—42no—
42C2×C4×C5×D3C2×C411yescharacteristic
43C2×C4×C5×D3C2×C411yescharacteristic
44C2×C4×C5×D3D411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C22×C3×Dic5—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48C2×#1204—21no—
49C2×D3×Dic5—21no—
50C2×D3×Dic5—21no—
51D3×Dic10—42no—
52C2×C3×C5×C8—21no—
53#6719—21no—
54C4⋊Dic15C2×C411yescharacteristic
55#6712—21no—
56C2×C5×C3⋊C8—21no—
57C5×ΓL(1,𝔽25)—42no—
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×#683—21no—
61Dic3⋊Dic5—21no—
62#6669—21no—
63#6668—21no—
64(C2×D3)⋊Dic5—24no—
65(C2×D3)⋊Dic5—21no—
66(C2×D3)⋊Dic5—21no—
67Dic3×Dic5—42no—
68D3×C22⋊Q8—51no—
69#4726D511yescharacteristic
70#4666—51no—
71C3×#328—51no—
72#4538—51no—
73#4467—51no—
74#4452—51no—
75C23×C4×C5—31no—
76C22×Dic10—31no—
77C2×C5×M16—61no—
78C2×C22⋊Dic5—61no—
79C2×C22⋊Dic5—61no—
80C2×C4⋊Dic5—31no—
81#4070—31no—
82#4070—31no—
83#4070—31no—
84#4070—61no—
85#4070—61no—
86#4070C2×D311yescharacteristic
87C2×#683—61no—
88C2×C4×Dic5—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92#3963—31no—
93#3963C2×D311yescharacteristic
94#1508—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—22no—
99C22×C5×D3—41no—
100C22×C5×D3C22⋊C411yescharacteristic
101C22×C5×D3C22⋊C411yescharacteristic
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×Dic15—22no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110Dic30—41no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3C22⋊C411yescharacteristic
113C2×C5×Dic3C22⋊C411yescharacteristic
114C4×C5×D3—22no—
115C4×C5×D3—22no—
116C4×C5×D3—41no—
117C4×C5×D3—41no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C3×Dic10—41no—
124#1204—42no—
125D3×Dic5—42no—
126D3×Dic5—42no—
127C3×C5×C8—41no—
128C5×C3⋊C8—41no—
129C2×D3×Q8—51no—
130C22×C4×D3C2×D511yescharacteristic
131C3×C22⋊Q8—51no—
132#946—51no—
133C2×(C2×D3)⋊C4—101no—
134#924—51no—
135C2×C4×Dic3—101no—
136C2×ΓL(1,𝔽25)—21no—
137#897—51no—
138#896—101no—
139D3×C4⋊C4—51no—
140D3×C4⋊C4—101no—
141D3×C22⋊C4—101no—
142#878—101no—
143C3×C22⋊C8C2×D511yescharacteristic
144C3×#95—51no—
145C3⋊#95—51no—
146#830C2×D511yescharacteristic
147(C2×D3)⋊C8—21no—
148C24×C5—31no—
149C22×C4×C5—31no—
150C22×C4×C5—31no—
151C22×C4×C5—31no—
152C22×C4×C5—31no—
153C22×C4×C5—31no—
154C22×C4×C5—122no—
155C22×C4×C5C22×D311yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—61no—
158C22×Dic5—61no—
159C22×Dic5—61no—
160C2×Dic10—31no—
161C2×Dic10—61no—
162C2×Dic10—122no—
163C2×Dic10C4×D311yescharacteristic
164C5×M16—122no—
165C2×C5×C8—21no—
166C2×C5×C8—61no—
167C22⋊Dic5—21no—
168C22⋊Dic5—61no—
169C22⋊Dic5—61no—
170C22⋊Dic5—64no—
171C22⋊Dic5—61no—
172C4⋊Dic5—31no—
173C4⋊Dic5—61no—
174C4⋊Dic5C4×D311yescharacteristic
175#683—21no—
176#683—61no—
177#683—61no—
178#683—61no—
179C4×Dic5—122no—
180C2×C22⋊Q8—151no—
181#407—31no—
182C4×C22⋊C4—151no—
183#328—51no—
184#328—151no—
185#328—151no—
186#328—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#13711yescharacteristic
191C22×C3×C5#13711yescharacteristic
192C2×C5×D3—21no—
193C2×C5×D3—21no—
194C2×C5×D3—21no—
195C2×C5×D3—21no—
196C2×C5×D3—21no—
197C2×C5×D3—42no—
198C2×C5×D3—42no—
199C2×C5×D3#10412yes—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202Dic15—42no—
203Dic15—41no—
204Dic15—41no—
205C3×Dic5—42no—
206C3×Dic5—41no—
207C3×Dic5—41no—
208C5×Dic3—21no—
209C5×Dic3#9912yes—
210C23×D3D2011yescharacteristic
211C2×C3×Q8—51no—
212C22×C3×C4—101no—
213C22×C3×C4C22×D511yescharacteristic
214C22×Dic3—101no—
215C22×Dic3D2011yescharacteristic
216D3×Q8—202no—
217C2×C4×D3—42no—
218C2×C4×D3—101no—
219C2×C4×D3—101no—
220C2×C4×D3C4×D511yescharacteristic
221C2×C4×D3C4×D511yescharacteristic
222C2×C4×D3C22⋊D511yescharacteristic
223C2×C4×D3C22⋊D511yescharacteristic
224C2×Dic6—51no—
225C2×Dic6—101no—
226C2×C3×C8—21no—
227C3×C4⋊C4—51no—
228C3×C4⋊C4—101no—
229C3×C22⋊C4—101no—
230#217—101no—
231(C2×D3)⋊C4—104no—
232(C2×D3)⋊C4—101no—
233(C2×D3)⋊C4—101no—
234C4⋊Dic3—51no—
235C4⋊Dic3—101no—
236Dic3⋊C4—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239C4×Dic3—202no—
240C2×C3⋊C8—21no—
241ΓL(1,𝔽25)—42no—
242C23×C5—31no—
243C23×C5—31no—
244C23×C5—62no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—121no—
248C23×C5D3×D411yescharacteristic
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—41no—
252C2×C4×C5—62no—
253C2×C4×C5—62no—
254C2×C4×C5—62no—
255C2×C4×C5—121no—
256C2×C4×C5—121no—
257C2×C4×C5C2×C4×D311yescharacteristic
258C2×C4×C5D3×D411yescharacteristic
259C2×Dic5—22no—
260C2×Dic5—21no—
261C2×Dic5—21no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264C2×Dic5—62no—
265C2×Dic5—61no—
266C2×Dic5—61no—
267C2×Dic5—122no—
268C2×Dic5—122no—
269C2×Dic5—121no—
270C2×Dic5—121no—
271Dic10—41no—
272Dic10—122no—
273Dic10—121no—
274C5×C8—41no—
275C5×C8—121no—
276C22×Q8—151no—
277C23×C4—31no—
278C2×M16—61no—
279C22⋊Q8—51no—
280C22⋊Q8—151no—
281C22⋊Q8—151no—
282C22⋊Q8—151no—
283C22⋊Q8—301no—
284C22⋊Q8—301no—
285C2×C4⋊C4—151no—
286C2×C4⋊C4—301no—
287C2×C22⋊C4—301no—
288C2×C22⋊C4—301no—
289C2×C42—301no—
290C22⋊C8—31no—
291C22⋊C8—61no—
292C22⋊C8D3×D511yescharacteristic
293#95—51no—
294#95—151no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5C2×#9911yescharacteristic
298C2×C3×C5#41911yescharacteristic
299C2×C3×C5C2×#10411yescharacteristic
300C5×D3—22no—
301C5×D3—41no—
302C23×C3C2×D2011yescharacteristic
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—22no—
306C22×D3—41no—
307C22×D3#68511yescharacteristic
308C22×D3#68511yescharacteristic
309C3×Q8—201no—
310C2×C3×C4—41no—
311C2×C3×C4—102no—
312C2×C3×C4—101no—
313C2×C3×C4—101no—
314C2×C3×C4—201no—
315C2×C3×C4—201no—
316C2×C3×C4C2×C4×D511yescharacteristic
317C2×C3×C4C2×C22⋊D511yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—102no—
320C2×Dic3—101no—
321C2×Dic3—101no—
322C2×Dic3—201no—
323C2×Dic3—201no—
324C2×Dic3#68511yescharacteristic
325C2×Dic3#68511yescharacteristic
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—41no—
329C4×D3—41no—
330C4×D3—202no—
331C4×D3—202no—
332Dic6—202no—
333Dic6—201no—
334C3×C8—41no—
335C3⋊C8—41no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—32no—
339C22×C5—61no—
340C22×C5—61no—
341C22×C5—61no—
342C22×C5—61no—
343C22×C5—61no—
344C22×C5—122no—
345C22×C5—122no—
346C22×C5D3×C22⋊C411yescharacteristic
347C22×C5#91511yescharacteristic
348C22×C5#91811yescharacteristic
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—32no—
352C4×C5—61no—
353Dic5—42no—
354Dic5—41no—
355Dic5—41no—
356Dic5—122no—
357Dic5—121no—
358Dic5—121no—
359C24—31no—
360C2×Q8—51no—
361C2×Q8—151no—
362C2×Q8—301no—
363C2×Q8—602no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—101no—
370C22×C4—122no—
371C22×C4—301no—
372C22×C4—301no—
373C22×C4—301no—
374C22×C4C2×D3×D511yescharacteristic
375M16—122no—
376C2×C8—21no—
377C2×C8—61no—
378C4⋊C4—51no—
379C4⋊C4—101no—
380C4⋊C4—151no—
381C4⋊C4—301no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C22⋊C4—101no—
386C22⋊C4—301no—
387C22⋊C4—301no—
388C22⋊C4—304no—
389C22⋊C4—301no—
390C42—602no—
391C3×C5#150811yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3#405511yescharacteristic
395C22×C3#405511yescharacteristic
396C22×C3C2×#68511yescharacteristic
397C2×D3—21no—
398C2×D3—21no—
399C2×D3—21no—
400C2×D3—21no—
401C2×D3—21no—
402C2×D3—42no—
403C2×D3—42no—
404C2×D3#395712yes—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—202no—
408C3×C4—201no—
409C3×C4—201no—
410Dic3—21no—
411Dic3—202no—
412Dic3—201no—
413Dic3—201no—
414Dic3#393812yes—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—62no—
418C2×C5—121no—
419C2×C5D3×#9911yescharacteristic
420C2×C5#480211yescharacteristic
421C2×C5D3×#10411yescharacteristic
422C23—31no—
423C23—31no—
424C23—62no—
425C23—61no—
426C23—61no—
427C23—121no—
428C23D3×D2011yescharacteristic
429Q8—201no—
430Q8—601no—
431Q8—602no—
432C2×C4—31no—
433C2×C4—31no—
434C2×C4—41no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—102no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—302no—
446C2×C4—301no—
447C2×C4—301no—
448C2×C4—602no—
449C2×C4—602no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4C4×D3×D511yescharacteristic
453C2×C4D3×C22⋊D511yescharacteristic
454C8—41no—
455C8—121no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3C2×#393811yescharacteristic
459C2×C3#6540911yescharacteristic
460C2×C3C2×#395711yescharacteristic
461D3—22no—
462D3—41no—
463C5#6833511yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—32no—
467C22—61no—
468C22—61no—
469C22—61no—
470C22—61no—
471C22—61no—
472C22—122no—
473C22—122no—
474C22#9126311yescharacteristic
475C22#9127411yescharacteristic
476C22D3×#68511yescharacteristic
477C4—21no—
478C4—21no—
479C4—32no—
480C4—61no—
481C4—202no—
482C4—201no—
483C4—201no—
484C4—602no—
485C4—601no—
486C4—601no—
487C3#1060077311yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—62no—
491C2—121no—
492C2D3×#393811yescharacteristic
493C2#1174812311yescharacteristic
494C2D3×#395711yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11746288C2semidirect
5. C3×#64687C2semidirect
6. #11745964C2semidirect
7. #11745960C2semidirect
10. C2×D3×Dic10C4semidirect
18. D3×C4⋊Dic5C4semidirect
20. #91369C4semidirect
21. #91365C4semidirect
35. #64687D3semidirect
391. C3×C5#1508semidirect
463. C5#68335semidirect
487. C3#10600773semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D3×#40702
C5×#47262
#117487192
#117462882
C3×#646872
#117459642
#117459602
#106007733
#683355